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High-order adaptive methods for parabolic systems. (English) Zbl 0790.65088
Adaptive methods for parabolic partial differential systems in one or two space dimensions are considered. The numerical solution is produced by finite element procedures that automatically refine and coarsen computational meshes, vary the degree of the piecewise polynomial basis, and, in one dimension, move the computational mesh.
Two-dimensional meshes of triangular, quadrilateral, or a mixture of triangular and quadrilateral elements are generated using a finite quadtree procedure that is also used for data management. A posteriori estimates, used to control adaptive enrichment, are generated from a hierarchical polynomial basis. Temporal integration, within a method of lines framework, uses either backward difference methods or a variant of singly implicit Runge-Kutta methods. A high level user interface facilitates the use of the adaptive software.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35K45 Initial value problems for second-order parabolic systems
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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